README

Copyright 2000, 2001, 2002 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.
The code in this directory works for Cray vector systems such as C90,
J90, T90 (both the CFP variant and the IEEE variant) and SV1. (For
the T3E and T3D systems, see the `alpha' subdirectory at the same
level as the directory containing this file.)
The cfp subdirectory is for systems utilizing the traditional Cray
floating-point format, and the ieee subdirectory is for the newer
systems that use the IEEE floating-point format.
There are several issues that reduces speed on Cray systems. For
systems with cfp floating point, the main obstacle is the forming of
128-bit products. For IEEE systems, adding, and in particular
computing carry is the main issue. There are no vectorizing
unsigned-less-than instructions, and the sequence that implement that
opetration is very long.
Shifting is the only operation that is simple to make fast. All Cray
systems have a bitblt instructions (Vi Vj,Vj<Ak and Vi Vj,Vj>Ak) that
should be really useful.
For best speed for cfp systems, we need a mul_basecase, since that
reduces the need for carry propagation to a minimum. Depending on the
size (vn) of the smaller of the two operands (V), we should split U and V
in different chunk sizes:
U split in 2 32-bit parts
V split according to the table:
parts 4 5 6 7 8
bits/part 16 13 11 10 8
max allowed vn 1 8 32 64 256
number of multiplies 8 10 12 14 16
peak cycles/limb 4 5 6 7 8
U split in 3 22-bit parts
V split according to the table:
parts 3 4 5
bits/part 22 16 13
max allowed vn 16 1024 8192
number of multiplies 9 12 15
peak cycles/limb 4.5 6 7.5
U split in 4 16-bit parts
V split according to the table:
parts 4
bits/part 16
max allowed vn 65536
number of multiplies 16
peak cycles/limb 8
(A T90 CPU can accumulate two products per cycle.)
IDEA:
* Rewrite mpn_add_n:
short cy[n + 1];
#pragma _CRI ivdep
for (i = 0; i < n; i++)
{ s = up[i] + vp[i];
rp[i] = s;
cy[i + 1] = s < up[i]; }
more_carries = 0;
#pragma _CRI ivdep
for (i = 1; i < n; i++)
{ s = rp[i] + cy[i];
rp[i] = s;
more_carries += s < cy[i]; }
cys = 0;
if (more_carries)
{
cys = rp[1] < cy[1];
for (i = 2; i < n; i++)
{ rp[i] += cys;
cys = rp[i] < cys; }
}
return cys + cy[n];
* Write mpn_add3_n for adding three operands. First add operands 1
and 2, and generate cy[]. Then add operand 3 to the partial result,
and accumulate carry into cy[]. Finally propagate carry just like
in the new mpn_add_n.
IDEA:
Store fewer bits, perhaps 62, per limb. That brings mpn_add_n time
down to 2.5 cycles/limb and mpn_addmul_1 times to 4 cycles/limb. By
storing even fewer bits per limb, perhaps 56, it would be possible to
write a mul_mul_basecase that would run at effectively 1 cycle/limb.
(Use VM here to better handle the romb-shaped multiply area, perhaps
rouding operand sizes up to the next power of 2.)